Analysis of Variance
Department of Educational Psychology
Agenda
1 Overview and Introduction
2 Decisions, Type I and Type II Errors, and Power
3 Identifying Assumption Violations
4 Conclusion
This module will help us introduce some of the problems and strategies that lead us to consider alternative analysis methods, like non-parametric tests, one of the foci of this semester
Students should be able to:
Last module, we left off talking about hypothesis testing, central to how we draw conclusions using inferential statistics.
With this module, we’ll review decision errors, and how we have to navigate possible issues that may inflate those types of errors, i.e., assumption violations
We’ll also cover some common strategies for looking for assumption violation, prior to next module, when we’ll work through fixing and addressing assumption violations
Agenda
1 Overview and Introduction
2 Decisions, Type I and Type II Errors, and Power
3 Identifying Assumption Violations
4 Conclusion
This section is review of module 1, please review that section if this terminology is unfamiliar
At the end of an inferential test, we will have a p-value and compare that with a pre-set alpha value
| Reality (Truth) | Decision: Reject H₀ | Decision: Fail to Reject H₀ |
|---|---|---|
| H₀ is True | Type I Error (α) False positive | Correct Decision (1 - β; power) (True negative) |
| H₁ is True | Correct Decision (1 - α) (True positive) | Type II Error (β) False negative |
As sample size (\(n\)) increases, power increases, this is rooted in the law of large numbers and central limit theorem, and how greater sample size contributes to less variability
With standard Error of mean, it is given as: \(\frac{\sigma}{\sqrt{N}}\), where:
Given the formula for the SE, an increase in \(N\) (in the denominator) decreases standard error for the mean, which results in less variability, and thus, more power
Agenda
1 Overview and Introduction
2 Decisions, Type I and Type II Errors, and Power
3 Identifying Assumption Violations
4 Conclusion
The homogeneity of variances assumption is the assumption that is each group’s measure is distributed roughly the same as one another, in the population
Histogram strategy
The independence assumption is an assumption that two variables or events are unrelated, and sampled independently from the two populations from which they belong
There is not a statistical test or realistic method in analysis to detect whether this is an issue or not \(\rightarrow\), more of an issue of research design
Agenda
1 Overview and Introduction
2 Decisions, Type I and Type II Errors, and Power
3 Identifying Assumption Violations
4 Conclusion
Our decision making in choosing to reject or retain the null hypothesis can be confounded by trying to avoid Type I and Type II errors, while still maintain adequate power to detect effects.
There are several ways to increase power in our study, with the most common method being increasing sample size
However, assumption violations can detract from our power, when using parametric tests, so we need to be wary of detecting those violations.
We introduced several useful methods by which to consider finding problems in normality or homogeneity of variances, while also briefly discussing independence.
Next week will involve a discussion and demonstration on how to address and possibly solve some assumption violation issues
Module 2 Lecture - Review of Inferential Statistics, Power, and Assumptions || Analysis of Variance